Protoalgebraic Logics: 10 (Trends in Logic, 10) - Hardcover

Czelakowski, Janusz

Hardcover

ISBN 10: 0792369408 ISBN 13: 9780792369400

Publisher: Springer, 2001

Synopsis

The main aim of this book is to present recent ideas in logic centered around the notion of a consequence operation. We wish to show these ideas in a factually and materially connected way, i.e., in the form of a consistent theory derived from several simple assumptions and definitions. These ideas have arisen in many research centers. The thorough study of their history can certainly be an exciting task for the historian of logic; in the book this aspect of the theory is being played down. The book belongs to abstract algebraic logic, the area of research that explores to a large extent interconnections between algebra and logic. The results presented here concern logics defined in zero-order languages (Le., quantifier-free sentential languages without predicate symbols). The reach of the theory expounded in the book is, in fact, much wider. The theory is also valid for logics defined in languages of higer orders. The problem of transferring the theory to the level of first-order languages has been satisfactorily solved and new ideas within this area have been put forward in the work of Blok and Pigozzi [1989].

About this title

Review

`This book is an excellent and very readable introduction to the area of abstract algebraic logic. It includes recent technical results together with philosophical comments to provide a context. Many of the chapters contain exercises that give additional results and all of the chapters contain extensive end notes to guide the reader to the literature '
Mathematical Reviews, 2002f

Synopsis

The main aim of this monograph is to provide a structured study of the algebraic method in metalogic. In contrast to traditional algebraic logic, where the focus is on the algebraic forms of specific deductive systems, abstract algebraic logic is concerned with the process of algebraization itself. This book presents in a systematic way recent ideas in abstract algebraic logic centered around the notion of the Leibniz operator. The stress is put on the taxonomy of deductive systems. Isolating a list of plausible properties of the Leibniz operator serves as a basis for distinguishing certain natural classes of sentential logics.The hierarchy of deductive systems presented in the book comprises, among others, the following classes: protoalgebraic logics, equivalential logics, algebraizable logics, and Fregean logics. Because of the intimate connection between algebraic and logical structures, the book also provides a uniform treatment of various topics concerning deduction theorems and quasivarieties of algebras. The presentation of the above classes of logics is accompanied by a wealth of examples illustrating the general theory.

An essential part of the book is formed by the numerous exercises integrated into the text. This book is both suitable for logically and algebraically minded graduate and advanced graduate students of mathematics, computer science and philosophy, and as a reference work for the expert.

Edition details

• Publisher: Springer
• Publication date: 2001
• ISBN 10: 0792369408
• ISBN 13: 9780792369400
• Binding: Hardcover
• Language: English
• Number of pages: 464